Impedance restrictions on independent finger grippers

The impedance matrices of independent point fingers of a multifingered gripper map to the impedance matrix of a grasped workpart. We find that in a planar geometry, three fingers are enough to allow an unrestricted range of workpart impedances, if finger impedances are selectable. In a spatial geometry however, five fingers are necessary for the broadest range of workpart impedances, and even so there is one impedance matrix that a workpart cannot attain regardless of the number of fingers that grasp it. We find this “unattainable” impedance matrix. We also characterize the impedance restrictions on workparts grasped with fewer than five spatial or three planar fingers